Loop Algorithm for Quantum Transverse Ising Model in a Longitudinal Field

TL;DR

This paper introduces a novel loop algorithm with a merge-unmerge process that significantly improves quantum Monte Carlo simulations of the transverse Ising model in a longitudinal field, especially for large fields and complex systems.

Contribution

The paper develops a new loop algorithm with a merge-unmerge process, enhancing simulation efficiency for the quantum transverse Ising model in a longitudinal field.

Findings

Demonstrates superior performance over existing algorithms in simulating Rydberg atom chains and Kagome qubit ice.

Effective in reducing auto-correlation in Monte Carlo steps.

Applicable to various quantum systems like Rydberg arrays, trapped ions, and quantum materials.

Abstract

The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem in most cases, the corresponding quantum Monte Carlo algorithm performs inefficiently, especially at a large longitudinal field. The main hindrance is the lack of loop update method which can strongly decrease the auto-correlation between Monte Carlo steps. Here, we successfully develop a loop algorithm with a novel merge-unmerge process. It demonstrates a great advantage over the state-of-the-art algorithm when implementing it to simulate the Rydberg atom chain and Kagome qubit ice. This advanced algorithm suits various systems such as Rydberg atom arrays, trapped ions, quantum materials, and quantum annealers.